Question

The set of ordered pairs shown below is a relation that is a function of x.

{(−3, 5)(−4, 7)(−6, 9) (−5, 11)}
Which ordered pair could be included in the set so that the relation remains a function of x?
A. (-5,15)
B. (-6,13)
C.(-9,7)
D.(-3,7)

Answer 1

The correct ordered pair that could be included in the set to maintain it as a function of x is C. (-9,7), because -9 is not already an x-value in the set.

Step-by-step explanation:

You are correct that the given set of ordered pairs {(-3, 5), (-4, 7), (-6, 9), (-5, 11)} is a function of x because each x-value is paired with exactly one y-value. To ensure that the relation remains a function when another ordered pair is added, we must avoid adding an ordered pair with an x-value that already exists in the set.

Looking at the options:

• A. (-5,15) - Cannot be included because the x-value -5 is already paired with 11.
• B. (-6,13) - Cannot be included because the x-value -6 is already paired with 9.
• C. (-9,7) - Can be included because the x-value -9 is not already in the set.
• D. (-3,7) - Cannot be included because the x-value -3 is already paired with 5.

Therefore, the correct answer is C. (-9,7), as adding this pair will allow the relation to stay a function of x.